Two-dimensional least-squares estimation for motion tracking in ultrasound elastography

Plane-wave transverse oscillation for high-frame-rate 2-D vector flow imaging

Transverse oscillation (TO) methods introduce oscillations in the pulse-echo field (PEF) along the direction transverse to the ultrasound propagation direction. This may be exploited to extend flow investigations toward multidimensional estimates. In this paper, the TOs are coupled with the transmission of plane waves (PWs) to reconstruct high-framerate RF images with bidirectional oscillations in the pulse-echo field. Such RF images are then processed by a 2-D phase-based displacement estimator to produce 2-D vector flow maps at thousands of frames per second. First, the capability of generating TOs after PW transmissions was thoroughly investigated by varying the lateral wavelength, the burst length, and the transmission frequency. Over the entire region of interest, the generated lateral wavelengths, compared with the designed ones, presented bias and standard deviation of -3.3 ± 5.7% and 10.6 ± 7.4% in simulations and experiments, respectively. The performance of the ultrafast vector flow mapping method was also assessed by evaluating the differences between the estimated velocities and the expected ones. Both simulations and experiments show overall biases lower than 20% when varying the beam-to-flow angle, the peak velocity, and the depth of interest. In vivo applications of the method on the common carotid and the brachial arteries are also presented.

Curl-Based Finite Element Reconstruction of the Shear Modulus Without Assuming Local Homogeneity: Time Harmonic Case

In elasticity imaging, the shear modulus is obtained from measured tissue displacement data by solving an inverse problem based on the wave equation describing the tissue motion. In most inversion approaches, the wave equation is simplified using local homogeneity and incompressibility assumptions. This causes a loss of accuracy and therefore imaging artifacts in the resulting elasticity images. In this paper we present a new curl-based finite element method inversion technique that does not rely upon these simplifying assumptions. As done in previous research, we use the curl operator to eliminate the dilatational term in the wave equation, but we do not make the assumption of local homogeneity. We evaluate our approach using simulation data from a virtual tissue phantom assuming time harmonic motion and linear, isotropic, elastic behavior of the tissue. We show that our reconstruction results are superior to those obtained using previous curl-based methods with homogeneity assumption. We also show that with our approach, in the 2-D case, multi-frequency measurements provide better results than single-frequency measurements. Experimental results from magnetic resonance elastography of a CIRS elastography phantom confirm our simulation results and further demonstrate, in a quantitative and repeatable manner, that our method is accurate and robust.

Analysis of motion tracking in echocardiographic image sequences: influence of system geometry and point-spread function

This paper focuses on motion tracking in echocardiographic ultrasound images. The difficulty of this task is related to the fact that echographic image formation induces decorrelation between the underlying motion of tissue and the observed speckle motion. Since Meunier's seminal work, this phenomenon has been investigated in many simulation studies as part of speckle tracking or optical flow-based motion estimation techniques. Most of these studies modeled image formation using a linear convolution approach, where the system point-spread function (PSF) was spatially invariant and the probe geometry was linear. While these assumptions are valid over a small spatial area, they constitute an oversimplification when a complete image is considered. Indeed, echocardiographic acquisition geometry relies on sectorial probes and the system PSF is not perfectly invariant, even if dynamic focusing is performed. This study investigated the influence of sectorial geometry and spatially varying PSF on speckle tracking. This was done by simulating a typical 64 elements, cardiac probe operating at 3.5 MHz frequency, using the simulation software Field II. This simulation first allowed quantification of the decorrelation induced by the system between two images when simple motion such as translation or incompressible deformation was applied. We then quantified the influence of decorrelation on speckle tracking accuracy using a conventional block matching (BM) algorithm and a bilinear deformable block matching (BDBM) algorithm. In echocardiography, motion estimation is usually performed on reconstructed images where the initial sectorial (i.e., polar) data are interpolated on a cartesian grid. We therefore studied the influence of sectorial acquisition geometry, by performing block matching on cartesian and polar data. Simulation results show that decorrelation is spatially variant and depends on the position of the region where motion takes place relative to the probe. Previous studies did not consider translation in their experiments, since their simulation model (spatially invariant PSF and linear probe) yields by definition no decorrelation. On the opposite, our realistic simulation settings (i.e., sectorial probe and realistic beamforming) show that translation yields decorrelation, particularly when translation is large (above 6 mm) and when the moving regions is located close to the probe (distance to probe less than 50 mm). The tracking accuracy study shows that tracking errors are larger for the usual cartesian data, whatever the estimation algorithm, indicating that speckle tracking is more reliable when based on the unconverted polar data: for axial translations in the range 0-10 mm, the maximum error associated to conventional block matching (BM) is 4.2 mm when using cartesian data and 1.8 mm for polar data. The corresponding errors are 1.8 mm (cartesian data) and 0.4 mm (polar data) for an applied deformation in the range 0-10%. We also show that accuracy is improved by using the bilinear deformable block matching (BDBM) algorithm. For translation, the maximum error associated to the bilinear deformable block matching is indeed 3.6mm (cartesian data) and 1.2 mm (polar data). Regarding deformation, the error is 0.7 mm (cartesian data) and 0.3 mm (polar data). These figures also indicates that the larger improvement brought by the bilinear deformable block matching over standard block matching logically takes place when deformation on cartesian data is considered (the error drops from 1.8 to 0.7 mm is this case). We give a preliminary evaluation of this framework on a cardiac sequence acquired with a Toshiba Powervision 6000 imaging system using a probe operating at 3.25 MHz. As ground truth reference motion is not available in this case, motion estimation performance was evaluated by comparing a reference image (i.e., the first image of the sequence) and the subsequent images after motion compensation has been applied. The comparison was quantified by computing the normalized correlation between the reference and the motion-compensated images. The obtained results are consistent with the simulation data: correlation is smaller for cartesian data, whatever the estimation algorithm. The correlation associated to the conventional block matching (BM) is in the range 0.45-0.02 when using cartesian data and in the range 0.65-0.2 for polar data. The corresponding correlation ranges for the bilinear deformable block matching are 0.98-0.2 and 0.98-0.55. In the same way these figures indicate that the bilinear deformable block matching yield a larger improvement when cartesian data are considered (correlation range increases from 0.45-0.02 to 0.98-0.2 in this case).